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My answer assumes you are specifically referring to the ideas of Heraclitus (the originator of Western ideas of Becoming). There are some interesting correlates between the origins of the Western idea of flux or becoming which was first articulated by the Greek philosopher Heraclitus and the Buddha's idea of Impermanence (Anicca). For Heraclitus ...
Everything flows and nothing stays.
Everything flows and nothing abides.
Everything gives way and nothing stays fixed.
Everything flows; nothing remains.
All is flux, nothing is stationary.
All is flux, nothing stays still.
All flows, nothing stays.No man ever steps in the same river twice.
There is subtle distinction between the Buddha and Heraclitus on the mechanism of change. For Buddha the process of change is driven by dependent origination - the idea that every phenomena exists entirely dependent on the causes that proceed it. Heraclitus had more of a transformative concept of change - that phenomena are the result of the tension and flux of the opposites. The end result is the same however - constant change.
So essentially there is very little difference between the Buddha's concept of Annica and Heraclitus's ideas of Becoming.
Other interesting similarities between Heraclitus and Buddha:
There are many articles and books dedicated to investigating the similarities between the views of Heraclitus and Buddha on the internet. Nice summary here - Heraclitus and the Buddha on Impermanence
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According to Buddhism the "Becoming" is define as create "Nama-Rupa".
The Alternatives for nāmarūpa is saṅkhāra.
All the sankaras are impermanence. That is called Anicca.
Definition for the pāli word Santati (line)
continuity of states rūpa˚ of form;
causal connection of material things“Empty is this, bhikkhus—the saṅkhāras—either of soul or of what belongs to soul”